This work intends to analyze the global threshold dynamics of an HIV infection model with age-space structure, latency and two transmission paths (virus to cell and cell to cell) under the Neumann boundary condition. The original model is converted into a hybrid system comprising two Volterra integral equations and two partial differential equations by integrating along the characteristic line. The well-posedness of the model is demonstrated by showing that the solution exists globally by virtue of the fixed point theory. In order to discuss whether the infection is persistent or extinct, we provide the explicit formulation of the basic reproduction number. By analyzing the roots distribution of the characteristic equations and constructing proper Lyapunov functionals, the local and global stability for different steady states are achieved. Numerical simulations are conducted to confirm our theoretical results.

中文翻译：

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具有感染年龄、潜伏期和细胞间传播的扩散性 HIV 感染模型的阈值动态


这项工作旨在分析诺依曼边界条件下具有年龄空间结构、潜伏期和两个传播路径（病毒到细胞和细胞到细胞）的 HIV 感染模型的全局阈值动态。通过沿特征线积分，将原始模型转换为由两个 Volterra 积分方程和两个偏微分方程组成的混合系统。通过不动点理论证明解全局存在，从而证明了模型的适定性。为了讨论感染是持续的还是灭绝的，我们提供了基本再生数的明确表述。通过分析特征方程的根分布并构造适当的Lyapunov泛函，实现了不同稳态下的局部和全局稳定性。进行数值模拟以证实我们的理论结果。